The Wikipedia article on it explains it nicely: Uniform convergence - Wikipedia, the free encyclopedia
hello to all
I have some issue of understanding this criteria... it says:
my question is why it is "uniformly" convergent ? I just can't see the fact why we have here uniformly convergent series...Let
be positive numerical sequence for which is worth that for almost every
and every
is satisfied that
then if series:
is convergent then series (of functions) :
is uniformly convergent on set A.
Thanks for any help
The Wikipedia article on it explains it nicely: Uniform convergence - Wikipedia, the free encyclopedia
I don't have a problem with understanding the meaning of uniform convergence... I have problem with this criteria... perhaps i was not clear about it very good... I'm also having problem with English hehehe
It's like this.... Why with assumption that (a_n) is sequence of positive numbers... and if ... (everything in the criteria) .... how someone can conclude that series of functions uniformly converge ... because of what ? Is it because of absolutely convergence of numerical series... ? or what ? how do I know that It's uniformly converge and not just by points...
check the proof
Weierstrass M-test - Wikipedia, the free encyclopedia